Question

753. Cracking the Safe

中文文档

Description

There is a safe protected by a password. The password is a sequence of n digits where each digit can be in the range [0, k - 1].

The safe has a peculiar way of checking the password. When you enter in a sequence, it checks the most recent n digits that were entered each time you type a digit.

• For example, the correct password is "345" and you enter in "012345":
  • After typing 0, the most recent 3 digits is "0", which is incorrect.
  • After typing 1, the most recent 3 digits is "01", which is incorrect.
  • After typing 2, the most recent 3 digits is "012", which is incorrect.
  • After typing 3, the most recent 3 digits is "123", which is incorrect.
  • After typing 4, the most recent 3 digits is "234", which is incorrect.
  • After typing 5, the most recent 3 digits is "345", which is correct and the safe unlocks.

Return _any string of minimum length that will unlock the safe at some point of entering it_.

 

Example 1:

Input: n = 1, k = 2
Output: "10"
Explanation: The password is a single digit, so enter each digit. "01" would also unlock the safe.

Example 2:

Input: n = 2, k = 2
Output: "01100"
Explanation: For each possible password:
- "00" is typed in starting from the 4th digit.
- "01" is typed in starting from the 1st digit.
- "10" is typed in starting from the 3rd digit.
- "11" is typed in starting from the 2nd digit.
Thus "01100" will unlock the safe. "10011", and "11001" would also unlock the safe.

 

Constraints:

• 1 <= n <= 4
• 1 <= k <= 10
• 1 <= kn <= 4096

Solutions

Solution 1

class Solution:
  def crackSafe(self, n: int, k: int) -> str:
    def dfs(u):
      for x in range(k):
        e = u * 10 + x
        if e not in vis:
          vis.add(e)
          v = e % mod
          dfs(v)
          ans.append(str(x))

    mod = 10 ** (n - 1)
    vis = set()
    ans = []
    dfs(0)
    ans.append("0" * (n - 1))
    return "".join(ans)

class Solution {
  private Set<Integer> vis = new HashSet<>();
  private StringBuilder ans = new StringBuilder();
  private int mod;

  public String crackSafe(int n, int k) {
    mod = (int) Math.pow(10, n - 1);
    dfs(0, k);
    ans.append("0".repeat(n - 1));
    return ans.toString();
  }

  private void dfs(int u, int k) {
    for (int x = 0; x < k; ++x) {
      int e = u * 10 + x;
      if (vis.add(e)) {
        int v = e % mod;
        dfs(v, k);
        ans.append(x);
      }
    }
  }
}

class Solution {
public:
  string crackSafe(int n, int k) {
    unordered_set<int> vis;
    int mod = pow(10, n - 1);
    string ans;
    function<void(int)> dfs = [&](int u) {
      for (int x = 0; x < k; ++x) {
        int e = u * 10 + x;
        if (!vis.count(e)) {
          vis.insert(e);
          dfs(e % mod);
          ans += (x + '0');
        }
      }
    };
    dfs(0);
    ans += string(n - 1, '0');
    return ans;
  }
};

func crackSafe(n int, k int) string {
  mod := int(math.Pow(10, float64(n-1)))
  vis := map[int]bool{}
  ans := &strings.Builder{}
  var dfs func(int)
  dfs = func(u int) {
    for x := 0; x < k; x++ {
      e := u*10 + x
      if !vis[e] {
        vis[e] = true
        v := e % mod
        dfs(v)
        ans.WriteByte(byte('0' + x))
      }
    }
  }
  dfs(0)
  ans.WriteString(strings.Repeat("0", n-1))
  return ans.String()
}